I think I understand the point you are trying to make, so these are responses to what I have interpreted from your post
The point about cutting out inflections making your voice seem boring seems reasonable, however I think what you are referring to is monotone. You still vary your pitch and speak with downward inflections without being monotonous. What Tom is trying to (I think) say is that you must not let those upward inflections dominate the entire interactions.
Sometimes, you are right, it can sound weird to eliminate ALL upward inflections in your speech. For instance, if you try asking a question without using one it can be very challenging, especially when in an interaction, to do so without sounding very weird.
If you watch the two recent infield video blog posts you will see that there is constant variation in tonality/inflections, but they are predominantly not using positive inflections.
As a general rule, "↗ Rising intonation" suggests uncertainty and need for assurance (a.k.a. approval seeking.) "↘ Falling intonation" demonstrates your confidence and certainty (making her the one who is having what she says affirmed by you).
Basically the gist of what I got from that small section was: don't make yourself seem uncertain, unconfident and unable supplicate what the girl says strongly - as Tom summed up nicely "Non-needy"
P.S. how did you get 4 gold coffee cups and VIP status? is it like a membership to the forum company thing or what :S?